Using \(x=\wp (\alpha )\)  as the coordinate on \(\Gamma /\mathbb {Z}_2\) , we also obtain \(\Phi =Ld\alpha = (\wp ^{\prime }(\alpha ))^{-1}Ldx\) . The properties of \(L\)  tell us that such \(\Phi \)  should be viewed as a Higgs field on the Riemann sphere with four marked points, more precisely, on an orbicurve \(\mathbb {CP}^1\)  of type \((2,2,2,2)\) . Recall [1]} that Hitchin systems on orbicurves can also be viewed as parabolic Hitchin systems, with (conjugacy classes of) the residues of \(\Phi \)  at the marked points being associated with the values of the moment map, cf. [2]}, [3]}. Therefore, the formula (REF ) should be interpreted as a parametrization, by \(p_i, q_i\) , of the corresponding \(2N\) -dimensional symplectic leaf of a parabolic \(\mathrm {SL}(2N, \mathbb {C})\)  Hitchin system on the Riemann sphere with four marked points \(e_i=\wp (\omega _i)\) , \(i=0, 1, 2, 3\) . This provides an interpretation of the Inozemtsev system as a Hitchin system. Note that this is different from the approach of [4]}. Note also that the pattern (REF )–() of the residues of \(\Phi \)  at the marked points is in good agreement with the SCFT picture (see Sec. REF  below). Also, as is explained below in Sec. REF , the genus of the spectral curve equals \(N\) , which is as expected from both the Hitchin-system and the M5-brane perspectives.
